Preface

Nonlinearities are ubiquitous and often incur twofold influence, which could be a source of troubles bringing uncertainty, inaccuracy, instability or even disaster in practice, and might also be a superior and beneficial factor for system performance improvement, energy cost reduction, safety maintenance or health monitoring, etc. Therefore, analysis and design of nonlinear systems are important and inevitable issues in both theoretical study and practical applications. Several methods are available in the literature to this aim including perturbation method, averaging method and harmonic balance method, etc. Nonlinear analysis can also be conducted in the frequency domain based on the Volterra series theory. The latter is a very useful tool with some special and beneficial features to tackle nonlinear problems. It is known that there is a considerably large class of nonlinear systems which allow a Volterra series expansion. Based on the Volterra series, the generalized frequency response function (GFRF) was defined as a multi-variate Fourier transform of the Volterra kernels in the 1950s. This presents a fundamental basis and therefore initiates a totally new theory or area for nonlinear analysis and design in the frequency domain. The frequency-domain nonlinear analysis theory and methods, based on the Volterra series approach, are observed with a faster development starting from the late 1980s or the early 1990s. Recursive algorithms for computation of the GFRFs for a given parametric nonlinear autoregressive with exogenous input (NARX) model or a given nonlinear differential equation (NDE) model are developed, and output frequency response of nonlinear systems and it properties are investigated accordingly. The area is becoming even more active in recent years. Much more efforts and progress can be seen in the development of applicationoriented theory and methods based on the GFRF concept. These include the concepts of nonlinear output spectrum (or output frequency response function) and nonlinear output frequency response function, parametric characteristic analysis, energy transfer properties and various applications in vibration control by exploring nonlinear benefits, fault detection, modelling and identification, data analysis and interpretation, etc.